Question

An oil tank is of the form of a cylinder with hemispherical ends. If the total length of tank is 19 m and the diameter of the cylinder is 7 m, find the amount of oil contains and its total surface area.

Answer 1

Given :

• An oil tank is of the form of a cylinder with hemispherical ends.
• Length of tank = 19 m
• Diameter of cylinder = 7 m

To Find :

• The amount of oil contained by oil tank i.e. volume of tank = ?
• Total surface area of tank = ?

Solution :

As, we have diameter of cylinder = 7 m

Hence, radius, r = 7/2 m = 3.5 m

Also,

radius of cylinder = radius of hemisphere = 3.5 m

Now, height of tank = 19 m

$\sf : \implies Height of cylinder = 19 - 2 \times 3.5 = 12 m$

Now,

TSA of the oil tank = CSA of the cylinder + SA of two hemisphere

$\sf : \implies TSA = 2\pi r h + 2(2\pi r^2)$

$\sf : \implies TSA = 2\times \dfrac{22}{7}\times 3.5 \times 12 + 2\Bigg( 2\times \dfrac{22}{7}\times (3.5)^2\Bigg)$

$\sf : \implies TSA = 2 \times 11\times 1\times 12 + 2\Bigg( 2\times \dfrac{22}{7}\times 12.25\Bigg)$

$\sf : \implies TSA = 264 + 2( 2\times 22 \times 1.75)$

$\sf : \implies TSA = 264 + 2(77)$

$\sf : \implies TSA = 264 + 154$

$\sf : \implies TSA = 418$

Hence, Total surface area of oil tanker = 418 m².

Now,

Volume of oil tanker = volume of the cylinder + volume of two hemisphere

$\sf : \implies Volume = \pi r^2 h + 2\Bigg(\dfrac{2}{3} \pi r^3\Bigg)$

$\sf : \implies Volume = \dfrac{22}{7}\times (3.5)^2 \times 12 + 2\Bigg(\dfrac{2}{3} \times \dfrac{22}{7}\times (3.5)^3\Bigg)$

$\sf : \implies Volume = \dfrac{22}{7}\times 12.25 \times 12 + 2\Bigg(\dfrac{2}{3} \times \dfrac{22}{7} \times 42.875 \Bigg)$

$\sf : \implies Volume = 462+ 2\Bigg(\dfrac{269.5}{3} \Bigg)$

$\sf : \implies Volume = \dfrac{1386 +539}{3}$

$\sf : \implies Volume = \dfrac{1925}{3}$

$\sf : \implies Volume = 641.67$

Hence, volume of oil tanker = 641.67 m³.